In this paper we follow a different path and carry out an a posteriori error analysis based on equilibrated tractions in the spirit of the Prager–Synge equality [1]} (see also [2]} and [3]}).
This approach, which does not require the saturation assumption when the dual norm of the residual is considered as an error measure, has also the advantage of avoiding unknown constants in the upper bound.
The corresponding error estimate can additionally be refined in order to distinguish the various components of the error (discretization, linearization, regularization).
This decomposition is leveraged here to design a fully adaptive resolution algorithm including an a posteriori-based stopping criterion for the nonlinear solver and the automatic tuning of the regularization parameter.
